Problem: Ashley is 40 years older than Michael. Five years ago, Ashley was 5 times as old as Michael. How old is Michael now?
Explanation: We can use the given information to write down two equations that describe the ages of Ashley and Michael. Let Ashley's current age be $a$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $a = m + 40$ Five years ago, Ashley was $a - 5$ years old, and Michael was $m - 5$ years old. The information in the second sentence can be expressed in the following equation: $a - 5 = 5(m - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = m + 40$ . Substituting this into our second equation, we get the equation: $(m + 40)$ $-$ $5 = 5(m - 5)$ which combines the information about $m$ from both of our original equations. Simplifying both sides of this equation, we get: $m + 35 = 5 m - 25$ Solving for $m$ , we get: $4 m = 60$ $m = 15$.